# Alligations and Mixtures Quiz Set 005

### Question 1

An electronics shop sold 24 TV sets at a 2% profit, and 4 Coolers at 23% profit. What is the average percentage profit earned by the shop?

A

5%.

B

6%.

C

4%.

D

8%.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average property of A1, and another sample n2 has an average property of A2, then the average property of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 23, A1 = 2, n1 = 24, n2 = 4, we have 24 × (A - 2) = 4 × (23 - A), from where we get A = 5%. The "property" in the alligation formula could be percentage, speed, weight, price, etc.,

### Question 2

A 300 liter mixture of milk and water contains 62% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

72 liter.

B

73 liter.

C

71 liter.

D

75 liter.

Soln.
Ans: a

The volume of milk will remain same at \${62 × 300}/100\$ = 186 liters. The amount of water at present is 300 - 186 = 114 liters. We need to make the volume of water equal to that of the milk. So we have to add 186 - 114 = 72 liters of water.

### Question 3

A milkman has 16 liters of 11% curd, and 4 liters of 21% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

A

13%.

B

14%.

C

12%.

D

16%.

Soln.
Ans: d

Quantities are equal, so answer = (11/100 + 21/100) X 100 = 16%.

### Question 4

21 Kg of Grade I sugar costing Rs. 24/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 4/Kg. What is the price of the mixture per Kg?

A

Rs. 18 per Kg.

B

Rs. 19 per Kg.

C

Rs. 17 per Kg.

D

Rs. 21 per Kg.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 4, A1 = 24, n1 = 21, n2 = 9, we have 21 × (A - 24) = 9 × (4 - A), from where we get A = Rs. 18 per Kg.

### Question 5

A mixture of milk and water contains 5 parts of milk and 1 parts of water. How much fraction of the mixture should be removed and replaced by water so that ratio of water and milk becomes equal?

A

\${2/5}\$.

B

\$1{3/4}\$.

C

\$1{5/7}\$.

D

\$2{3/7}\$.

Soln.
Ans: a

Let the volume of the mixture be 5 + 1 = 6 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$1 - {1x}/6 + x\$. The volume of the milk in the new mixture would be \$5 - {5x}/6.\$ Equating the two volumes and solving for x we get x = \${6 × 4}/{2 × 5}\$. The fraction that must be removed = \$1/6\$ × \${6 × 4}/{2 × 5}\$, which gives \$4/{2 × 5}\$ = \${2/5}\$. 